# Courses in Statistics (Division 489)

270. The Art of Scientific Investigation. (4). (NS).

The objective of this course is to introduce students to learning in a non-deterministic environment. An appreciation for measurement, bias and variation is essential to formulate questions and learn about things. Underlying this course is the Edwards Deming philosophy. Deming, an American statistician, was invited to Japan in the early 1950's to help improve the quality of mass produced items. His success in Japan is, in part, responsible for our current balance of trade deficit; and here, the Ford Motor Co., has also attained a larger market share as a result of his ideas. Implementation of the Deming message requires a critical appreciation of variation and the scientific method. Specifically, we will discuss: (1) Historical attempts to learn and the advent of the modern scientific method. (2) The differences between special or assignable causes and common causes of variation. Before we can learn how a process operates, the process must be stable. (3) Differences between observational and controlled randomized studies and associated ethical issues. (4) The 'what' and 'how' of measurement and the quantification of uncertainty-subjective and frequency notions of probability. (5) Understanding bias and variation. (6) How to use bias to design efficient studies. (7) Differences between enumerative and analytic studies. Many of the ideas will be introduced through experimentation (e.g., the red bead and funnel experiments) and the mathematical level will not require more than a modest background in high school algebra. The course format includes 3 lectures and a laboratory (1.5 hours per week). (Rothman)

300. Introduction to Statistical Reasoning. (3). (NS).

This course is designed to provide an overview of the field of statistics. Course topics include methods of analyzing and summarizing data, statistical reasoning as a means of learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Basic fallacies in common statistical analyses and reasoning are discussed and proper methods indicated. Alternative approaches to statistical inference are also discussed. The course emphasis is on presenting basic underlying concepts rather than on covering a wide variety of different methodologies. Evaluation is based upon a midterm and a final examination. The course format is lecture with some discussion.

311/I.O.E. 365. Engineering Statistics. Math. 215 and Eng. 102, or equivalent. No credit granted to those who have completed 412. (4). (Excl).

Analysis of engineering data associated with stochastic industrial processes. Topics include: fundamentals of distribution analyses; process model identification, estimation, testing of hypothesis, validation procedures, and evaluation of models by regression and correlation. Students are required to use the MTS computer system for problem solving.

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed 412. (4). (NS).

In this course students are introduced to the concepts and applications of statistical methods and data analysis. Statistics 402 has no prerequisite and has been elected by students whose mathematics background includes only high school algebra. Examples of applications are drawn from virtually all academic areas and some attention is given to statistical process control methods. The course format includes three lectures and a laboratory (l.5 hours per week). The laboratory section covers some of the data analysis material and introduces the use of interactive computing through the use of MIDAS. Course evaluation is based on a combination of three examinations GIVEN WEDNESDAY EVENINGS, a final examination and teaching fellow input.

403. Introduction to Statistics and Data Analysis II. Stat. 402. (4). (NS).

APPLIED REGRESSION. The course will also cover various topics associated with the general linear model emphasizing applications. Topics include: multiple regression, variable selection, stepwise regression, residual analysis, analysis of variance models, covariance analysis and principal components. OTHER TOPICS. As time allows, the course may cover some aspects of probit and logit analyses, analysis of time series data, reliability analysis, and topics in experimental design. Three hours of lecture and one and one-half hours of lab per week.

405./Econ. 405. Introduction to Statistics. Math. 115 or permission of instructor. Junior and seniors may elect concurrently with Econ. 201 and 202. No credit granted to those who have completed Econ. 404. (4). (SS).

Principles of statistics inference, including: probability, experimental and theoretic derivation of sampling distributions, hypothesis testing, estimation, and simple regression.

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and either CS 283 or Engin. 102. No credit granted to those who have completed 311 or 402. (3). (NS).

The objectives of this course are to introduce students to the basic ideas of probability and statistical inference and to acquaint students with some important data analytic techniques, such as regression and the analysis of variance. Examples will emphasize applications to the natural sciences and engineering. There will be regular homework, including assignments which require the use of MTS, two midterms, and a final exam.

425/Math. 425. Introduction to Probability. Math. 215. (3). (N.Excl).

See Math 425 for description.

426. Introduction to Mathematical Statistics. Stat. 425. (3). (NS).

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference. The sequence of Statistics 425/426 serves as a prerequisite for more advanced Statistics courses. Weekly problem sets, two hourly exams, and one final exam.

466/IOE 466. Statistical Quality Control. Statistics 311 or IOE 365. (3). (Excl).

Design and analysis of procedures for forecasting and control of production processes. Topics include: attribute and variables; sampling plans; sequential sampling plans; rectifying control procedures; charting, smoothing, forecasting, and prediction of discrete time series.

470. The Design of Scientific Experiments. Stat. 311, 402, 412, or 426; or permission of instructor. (4). (N.Excl).

The objective of this course is to introduce students to the process of planning, designing and implementation of a study. Includes enumerative, Monte Carlo, observational and controlled randomized experimentation. Emphasis is on the conceptual framework not on the mathematical theory of design (e.g., Statistics 570).

511. Mathematical Statistics II. Stat. 510. (3). (Excl).

Topics covered will include: hypothesis testing and related topics such as size, power, similarity and optimality properties. Likelihood ratio tests, generalized likelihood ratio tests, decision theory and Bayes approaches. Sequential procedures, large sample theory and various other topics. (Belisle)

525(510)/Math. 525. Probability Theory. Math. 450 or 451; or permission of instructor. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only 1 credit. (3). (N.Excl).

See Math 525 for description.

526/Math. 526/C.I.C.E. 516. Discrete State Stochastic Processes. Math. 525; or Stat. 525; or C.I.C.E. 512. (3). (N.Excl).

Generating functions: recurrent events and the renewal theorem; random walks. Markov chains; branching processes; limit theorems; Markov chains in continuos time with emphasis on birth and death processes and queueing theory. An introduction to Brownian motion, stationary processes and martingales.

531. Statistical Analysis of Time Series. Stat. 426. (3). (NS).

The major topics include time- and frequency-domain characteristics of stationary discrete time series, autoregressive and moving average models, prediction theory, estimation and hypothesis testing, and computer applications. Special topics might include vector autoregression, cross-spectral analysis, causality testing or other issues of current interest. Statistics 511 or Economics 775 is the standard prerequisite. Student evaluation is based on exams, homework, and a term paper. Lectures and problem sets including computer exercises are the main methods of instruction. (Howrey)

552. Sequential Analysis and Design. Stat. 426 or equivalent. (3). (NS).

Models for sequential sampling and sequential design; potential advantages and disadvantages of sequential methods, including their increased efficiency, ethical considerations, and the effect on significance levels; the insensitivity of the likelihood function and posterior distributions to sequential sampling; fixed width confidence intervals; the Robbins-Monro and related processes; some common sequential tests, including the sequential probability ratio test and restricted sequential procedures; decision theoretic formulation of sequential problems; Bayesian solutions of sequential problems by dynamic programming; applications to quality control and clinical trials; special topics.

560/Biostat. 685 (Public Health). Introduction to Nonparametric Statistics. Stat. 426 or permission of instructor. (3). (NS).

The course will cover the basic linear rank statistics for one sample, two sample, one and two way ANOVA, and regression problems. Tests and their power functions, point and interval estimates are covered. Efficiencies of rank and parametric tests are computed.

570. Experimental Design. Stat. 426 and a basic knowledge of matrix algebra; or permission of instructor. (3). (NS).

Basic topics and ideas in the design of experiments: randomization and randomization tests; the validity and analysis of randomized experiments; randomized blocks; Latin and Graeco-Latin squares; plot techniques; factorial experiments; the use of confounding and response surface methodology; weighing designs, lattice and incomplete block and partially balanced incomplete block designs.

576/Econ. 776. Econometric Theory II. Econ. 775 or equivalent. (3). (NS).

This is a course in advanced econometrics. It includes a thorough treatment of statistical problems in dealing with time series and cross-section data, a development of simultaneous equation techniques, and formulation and estimation of special models. Other topics may also be included depending on time and interest.